Definition 72.7.6. Let $S$ be a scheme. A big fppf site $(\textit{Spaces}/S)_{fppf}$ is any site constructed as follows:

1. Choose a big fppf site $(\mathit{Sch}/S)_{fppf}$ as in Topologies, Section 34.7.

2. As underlying category take the category $\textit{Spaces}/S$ of algebraic spaces over $S$ (see discussion in Section 72.2 why this is a set).

3. Choose any set of coverings as in Sets, Lemma 3.11.1 starting with the category $\textit{Spaces}/S$ and the class of fppf coverings of Definition 72.7.1.

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